A multicenter clinical trial is designed to evaluate the efficacy of newly formulated lipi… — USMLE Step 3

A multicenter clinical trial is designed to evaluate the efficacy of newly formulated lipid-lowering regimens in patients with familial hypercholesterolemia. The study randomizes 360 patients equally into 6 distinct treatment arms: high-intensity statin monotherapy, statin plus ezetimibe, statin plus a PCSK9 inhibitor, statin plus bempedoic acid, PCSK9 inhibitor monotherapy, and a placebo group.

After 12 weeks, an initial one-way analysis of variance (ANOVA) reveals a statistically significant difference in the mean percentage reduction of LDL cholesterol across the groups ( $p = 0.004$ ). The investigators plan to conduct post-hoc pairwise comparisons using independent $t$ -tests to identify which specific groups differ from one another. To control the family-wise Type I error rate at $\alpha = 0.05$ , they apply a Bonferroni correction by dividing the overall $\alpha$ by the total number of unique pairwise comparisons.

How many unique pairwise comparisons can be made among the treatment arms in this study?

Cevap: 15 comparisons

Cevap

In the context of post-hoc testing following a significant ANOVA, comparing all possible pairs of groups requires calculating the number of unique combinations of 2 items from a total of

k

items. The mathematical formula for this is

\binom{k}{2}

, which simplifies to

\frac{k(k-1)}{2}

. Given that there are 6 distinct treatment arms in this clinical trial, the calculation is

\frac{6 \times 5}{2} = 15

. Consequently, the investigators must divide their target overall

\alpha

(0.05) by 15 when performing the Bonferroni correction to maintain the family-wise error rate.

Adım Adım Çözüm

Identify the total number of distinct treatment groups (

k

k = 6

The stem describes 6 distinct treatment arms (statin alone, statin plus ezetimibe, statin plus PCSK9 inhibitor, statin plus bempedoic acid, PCSK9 inhibitor alone, and placebo).

Select the correct statistical formula for calculating the number of pairwise comparisons.

The number of unique pairs is given by the combination formula

\binom{k}{2} = \frac{k(k-1)}{2}

We are selecting 2 groups at a time from a total of

k

groups to run a

t

-test, and the order in which we select them does not matter.

Substitute the value of

k

into the formula and solve.

\frac{6 \times (6 - 1)}{2} = \frac{6 \times 5}{2} = \frac{30}{2} = 15

This yields the final count of unique pairwise comparisons required to perform the Bonferroni correction.

Anahtar Kavram

Calculating the number of pairwise comparisons for post-hoc testing

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